We can think of a number $n$ as a collection of $n$ blocks (or marbles, dominoes, or any other countable objects).

Numbers from 1 to 10:

o

oo

ooo

oooo

ooooo

oooooo

ooooooo

oooooooo

ooooooooo

oooooooooo

An even number can be divided into two equal parts, while an odd number cannot. Halving an odd number leaves a remainder of 1.

o

o
o

oo
o

oo
oo

ooo
oo

ooo
ooo

oooo
ooo

oooo
oooo

ooooo
oooo

ooooo
ooooo

Definition (Even and odd numbers): Let $n$ and $k$ be integers. We say that $n$ is even if there exists $k$ such that $n=2k$, and $n$ is odd if there exists $k$ such that $n=2k+1$.

Three doors have a middle one; four don't. However, if the three doors form a triangle, it wouldn't be obvious which one is the middle. A set with an odd number of elements has a middle element if the elements are "arranged in a line". Such an ordering seems to be called a linear order (or total order).